U.S. patent application number 14/526304 was filed with the patent office on 2015-06-18 for neuronal diversity in spiking neural networks and pattern classification.
The applicant listed for this patent is QUALCOMM Incorporated. Invention is credited to Vikram GUPTA, Jeffrey Alexander LEVIN, Edward Hanyu LIAO.
Application Number | 20150170027 14/526304 |
Document ID | / |
Family ID | 53368904 |
Filed Date | 2015-06-18 |
United States Patent
Application |
20150170027 |
Kind Code |
A1 |
GUPTA; Vikram ; et
al. |
June 18, 2015 |
NEURONAL DIVERSITY IN SPIKING NEURAL NETWORKS AND PATTERN
CLASSIFICATION
Abstract
A method for providing diversity in a set of neurons in a neuron
model includes retrieving a set of parameters for the set of
neurons. The method also includes perturbing the set of parameters
based on a neuron identification value, a level of perturbation for
each parameter and/or parameter values.
Inventors: |
GUPTA; Vikram; (San Diego,
CA) ; LEVIN; Jeffrey Alexander; (San Diego, CA)
; LIAO; Edward Hanyu; (San Diego, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
QUALCOMM Incorporated |
San Diego |
CA |
US |
|
|
Family ID: |
53368904 |
Appl. No.: |
14/526304 |
Filed: |
October 28, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61916030 |
Dec 13, 2013 |
|
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|
61916062 |
Dec 13, 2013 |
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Current U.S.
Class: |
706/25 |
Current CPC
Class: |
G06N 3/08 20130101; G06N
3/049 20130101 |
International
Class: |
G06N 3/08 20060101
G06N003/08 |
Claims
1. A method for providing diversity in a set of neurons in a neuron
model comprising: retrieving a set of parameters for the set of
neurons; and perturbing the set of parameters based at least in
part on a neuron identification value, a level of perturbation for
each parameter and/or parameter values.
2. The method of claim 1, in which the perturbing is based at least
in part on a percentage range of perturbation around a mean value
of at least one parameter value.
3. The method of claim 1, in which the perturbing includes
dithering at least a significant bit of a parameter value for at
least a portion of the set of neurons.
4. The method of claim 1, in which the level of perturbation of the
set of parameters is based at least in part on network behavior and
input statistics.
5. The method of claim 1, in which the level of perturbation of the
set of parameters is based at least in part on desired output.
6. The method of claim 1, in which the perturbing is based at least
in part on a desired probability distribution.
7. The method of claim 1, in which the level of perturbation of the
set of parameters is based at least in part on a level of diversity
in spike times.
8. The method of claim 1, in which the level of perturbation of the
set of parameters is based at least in part on a level of diversity
in synaptic weights.
9. An apparatus for providing diversity in a set of neurons in a
neuron model comprising: a memory; and at least one processor
coupled to the memory, the at least one processor being configured:
to retrieve a set of parameters for the set of neurons; and to
perturb the set of parameters based at least in part on a neuron
identification value, a level of perturbation for each parameter
and/or parameter values.
10. The apparatus of claim 9, in which the at least one processor
is further configured to perturb the set of parameters based at
least in part on a percentage range of perturbation around a mean
value of at least one parameter value.
11. The apparatus of claim 9, in which the at least one processor
is further configured to dither at least a significant bit of a
parameter value for at least a portion of the set of neurons.
12. The apparatus of claim 9, in which the level of perturbation of
the set of parameters is based at least in part on network behavior
and input statistics.
13. The apparatus of claim 9, in which the level of perturbation of
the set of parameters is based at least in part on desired
output.
14. The apparatus of claim 9, in which the at least one processor
is further configured to perturb the set of parameters based at
least in part on a desired probability distribution.
15. The apparatus of claim 9, in which the level of perturbation of
the set of parameters is based at least in part on a level of
diversity in spike times.
16. The apparatus of claim 9, in which the level of perturbation of
the set of parameters is based at least in part on a level of
diversity in synaptic weights.
17. An apparatus for providing diversity in a set of neurons in a
neuron model comprising: means for retrieving a set of parameters
for the set of neurons; and means for perturbing the set of
parameters based at least in part on a neuron identification value,
a level of perturbation for each parameter and/or parameter
values.
18. The apparatus of claim 17, in which the means for perturbing
perturbs the set of parameters based at least in part on a
percentage range of perturbation around a mean value of at least
one parameter value.
19. The apparatus of claim 17, in which the means for perturbing
dithers at least a significant bit of a parameter value for at
least a portion of the set of neurons.
20. The apparatus of claim 17, in which the level of perturbation
of the set of parameters is based at least in part on network
behavior and input statistics.
21. The apparatus of claim 17, in which the level of perturbation
of the set of parameters is based at least in part on desired
output.
22. The apparatus of claim 17, in which the means for perturbing
perturbs the set of parameters based at least in part on a desired
probability distribution.
23. The apparatus of claim 17, in which the level of perturbation
of the set of parameters is based at least in part on a level of
diversity in spike times.
24. The apparatus of claim 17, in which the level of perturbation
of the set of parameters is based at least in part on a level of
diversity in synaptic weights.
25. A computer program product for providing diversity in a set of
neurons in a neuron model comprising: a non-transitory computer
readable medium having encoded thereon program code, the program
code comprising: program code to retrieve a set of parameters for
the set of neurons; and program code to perturb the set of
parameters based at least in part on a neuron identification value,
a level of perturbation for each parameter and/or parameter
values.
26. The computer program product of claim 25, further comprising
program code to perturb the set of parameters based at least in
part on a percentage range of perturbation around a mean value of
at least one parameter value.
27. The computer program product of claim 25, further comprising
program code to dither at least a significant bit of a parameter
value for at least a portion of the set of neurons.
28. The computer program product of claim 25, in which the level of
perturbation of the set of parameters is based at least in part on
network behavior and input statistics.
29. The computer program product of claim 25, in which the level of
perturbation of the set of parameters is based at least in part on
desired output.
30. The computer program product of claim 25, further comprising
program code to perturb the set of parameters based at least in
part on a desired probability distribution.
31. The computer program product of claim 25, in which the level of
perturbation of the set of parameters is based at least in part on
a level of diversity in spike times.
32. The computer program product of claim 25, in which the level of
perturbation of the set of parameters is based at least in part on
a level of diversity in synaptic weights.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] The present application claims the benefit of U.S.
Provisional Patent Application No. 61/916,030, filed on Dec. 13,
2013, titled "NEURONAL DIVERSITY IN SPIKING NEURAL NETWORKS AND
PATTERN CLASSIFICATION," and U.S. Provisional Patent Application
No. 61/916,062, filed on Dec. 13, 2013, titled "NEURONAL DIVERSITY
IN SPIKING NEURAL NETWORKS AND PATTERN CLASSIFICATION," the
disclosures of which are expressly incorporated by reference herein
in their entireties.
BACKGROUND
[0002] 1. Field
[0003] Certain aspects of the present disclosure generally relate
to neural system engineering and, more particularly, to systems and
methods for providing neuronal diversity in a spiking neural
network.
[0004] 2. Background
[0005] An artificial neural network, which may comprise an
interconnected group of artificial neurons (i.e., neuron models),
is a computational device or represents a method to be performed by
a computational device. Artificial neural networks may have
corresponding structure and/or function in biological neural
networks.
[0006] In typical artificial neural networks, parallel processing
may be achieved by connecting many neurons from a single layer to
many neurons in another layer. Similar connectivity is observed in
biology in the neo-cortex. The neurons belonging to a layer of the
artificial neural networks may be configured with similar, if not
identical parameters. Likewise, the neurons in a layer may be found
to have a similar structure, (e.g., pyramidal neurons (triangular
shaped structure), or basket neurons (basket shaped structure)).
When using a spiking neural network, the input signal to each
neuron of a layer may be differentiated by applying different
delays to the inputs.
[0007] Diversity in synaptic delays is also observed in biology and
may be useful when the input signal uses temporal coding. However,
simply varying synaptic delays may not utilize the rich non-linear
neuronal dynamics. Viewing from a signal processing point of view,
having different synaptic delays may only shift the incoming signal
temporally, but may not modulate these signals in any manner.
However, if the neurons in the output layer of the network were to
spike for different inter-spike intervals between the two incoming
spikes, or spike at different times even when the spikes are
received exactly at the same time, the output from these two
neurons will be quite different. Such neurons may provide a much
richer level of signal processing than what is possible if both had
exactly the same parameters.
SUMMARY
[0008] In an aspect of the present disclosure, a method for
providing diversity in a set of neurons in a neuron model is
disclosed. The method includes retrieving a set of parameters for
the set of neurons. The method also includes perturbing the set of
parameters based on a neuron identification value, a level of
perturbation for each parameter and/or parameter values.
[0009] In another aspect of the present disclosure, an apparatus
for providing diversity in a set of neurons in a neuron model is
disclosed. The apparatus includes a memory and one or more
processors coupled to the memory. The processor(s) is(are)
configured to retrieve a set of parameters for the set of neurons.
The processor(s) is(are) also configured to perturb the set of
parameters based on a neuron identification value, a level of
perturbation for each parameter and/or parameter values.
[0010] In yet another aspect of the present disclosure, an
apparatus for providing diversity in a set of neurons in a neuron
model is disclosed. The apparatus includes means for retrieving a
set of parameters for the set of neurons. The apparatus also
includes means for perturbing the set of parameters based on a
neuron identification value, a level of perturbation for each
parameter and/or parameter values.
[0011] In still another aspect of the present disclosure, a
computer program product for providing diversity in a set of
neurons in a neuron model is presented. The computer program
product includes a non-transitory computer readable medium having
encoded thereon program code. The program code includes program
code to retrieve a set of parameters for the set of neurons. The
program code also includes program code to perturb the set of
parameters based on a neuron identification value, a level of
perturbation for each parameter and/or parameter values.
[0012] This has outlined, rather broadly, the features and
technical advantages of the present disclosure in order that the
detailed description that follows may be better understood.
Additional features and advantages of the disclosure will be
described below. It should be appreciated by those skilled in the
art that this disclosure may be readily utilized as a basis for
modifying or designing other structures for carrying out the same
purposes of the present disclosure. It should also be realized by
those skilled in the art that such equivalent constructions do not
depart from the teachings of the disclosure as set forth in the
appended claims. The novel features, which are believed to be
characteristic of the disclosure, both as to its organization and
method of operation, together with further objects and advantages,
will be better understood from the following description when
considered in connection with the accompanying figures. It is to be
expressly understood, however, that each of the figures is provided
for the purpose of illustration and description only and is not
intended as a definition of the limits of the present
disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The features, nature, and advantages of the present
disclosure will become more apparent from the detailed description
set forth below when taken in conjunction with the drawings in
which like reference characters identify correspondingly
throughout.
[0014] FIG. 1 illustrates an example network of neurons in
accordance with certain aspects of the present disclosure.
[0015] FIG. 2 illustrates an example of a processing unit (neuron)
of a computational network (neural system or neural network) in
accordance with certain aspects of the present disclosure.
[0016] FIG. 3 illustrates an example of spike-timing dependent
plasticity (STDP) curve in accordance with certain aspects of the
present disclosure.
[0017] FIG. 4 illustrates an example of a positive regime and a
negative regime for defining behavior of a neuron model in
accordance with certain aspects of the present disclosure.
[0018] FIG. 5 illustrates an example implementation of designing a
neural network using a general-purpose processor in accordance with
certain aspects of the present disclosure.
[0019] FIG. 6 illustrates an example implementation of designing a
neural network where a memory may be interfaced with individual
distributed processing units in accordance with certain aspects of
the present disclosure.
[0020] FIG. 7 illustrates an example implementation of designing a
neural network based on distributed memories and distributed
processing units in accordance with certain aspects of the present
disclosure.
[0021] FIG. 8 illustrates an example implementation of a neural
network in accordance with certain aspects of the present
disclosure.
[0022] FIG. 9A is a block diagram illustrating an exemplary neural
network implementing neural diversity in accordance with aspects of
the present disclosure.
[0023] FIG. 9B illustrates spike time diversity and weight
diversity in accordance with aspects of the present disclosure.
[0024] FIG. 10 is a block diagram illustrating an exemplary neural
network using neural diversity to provide pattern classification in
accordance with aspects of the present disclosure.
[0025] FIG. 11 illustrates a method for providing neuronal
diversity in a set of neurons in accordance with aspects of the
present disclosure.
[0026] FIG. 12 illustrates a method for pattern recognition in a
spiking neural network in accordance with aspects of the present
disclosure.
DETAILED DESCRIPTION
[0027] The detailed description set forth below, in connection with
the appended drawings, is intended as a description of various
configurations and is not intended to represent the only
configurations in which the concepts described herein may be
practiced. The detailed description includes specific details for
the purpose of providing a thorough understanding of the various
concepts. However, it will be apparent to those skilled in the art
that these concepts may be practiced without these specific
details. In some instances, well-known structures and components
are shown in block diagram form in order to avoid obscuring such
concepts.
[0028] Based on the teachings, one skilled in the art should
appreciate that the scope of the disclosure is intended to cover
any aspect of the disclosure, whether implemented independently of
or combined with any other aspect of the disclosure. For example,
an apparatus may be implemented or a method may be practiced using
any number of the aspects set forth. In addition, the scope of the
disclosure is intended to cover such an apparatus or method
practiced using other structure, functionality, or structure and
functionality in addition to or other than the various aspects of
the disclosure set forth. It should be understood that any aspect
of the disclosure disclosed may be embodied by one or more elements
of a claim.
[0029] The word "exemplary" is used herein to mean "serving as an
example, instance, or illustration." Any aspect described herein as
"exemplary" is not necessarily to be construed as preferred or
advantageous over other aspects.
[0030] Although particular aspects are described herein, many
variations and permutations of these aspects fall within the scope
of the disclosure. Although some benefits and advantages of the
preferred aspects are mentioned, the scope of the disclosure is not
intended to be limited to particular benefits, uses or objectives.
Rather, aspects of the disclosure are intended to be broadly
applicable to different technologies, system configurations,
networks and protocols, some of which are illustrated by way of
example in the figures and in the following description of the
preferred aspects. The detailed description and drawings are merely
illustrative of the disclosure rather than limiting, the scope of
the disclosure being defined by the appended claims and equivalents
thereof.
An Example Neural System, Training and Operation
[0031] FIG. 1 illustrates an example artificial neural system 100
with multiple levels of neurons in accordance with certain aspects
of the present disclosure. The neural system 100 may have a level
of neurons 102 connected to another level of neurons 106 through a
network of synaptic connections 104 (i.e., feed-forward
connections). For simplicity, only two levels of neurons are
illustrated in FIG. 1, although fewer or more levels of neurons may
exist in a neural system. It should be noted that some of the
neurons may connect to other neurons of the same layer through
lateral connections. Furthermore, some of the neurons may connect
back to a neuron of a previous layer through feedback
connections.
[0032] As illustrated in FIG. 1, each neuron in the level 102 may
receive an input signal 108 that may be generated by neurons of a
previous level (not shown in FIG. 1). The signal 108 may represent
an input current of the level 102 neuron. This current may be
accumulated on the neuron membrane to charge a membrane potential.
When the membrane potential reaches its threshold value, the neuron
may fire and generate an output spike to be transferred to the next
level of neurons (e.g., the level 106). In some modeling
approaches, the neuron may continuously transfer a signal to the
next level of neurons. This signal is typically a function of the
membrane potential. Such behavior can be emulated or simulated in
hardware and/or software, including analog and digital
implementations such as those described below.
[0033] In biological neurons, the output spike generated when a
neuron fires is referred to as an action potential. This electrical
signal is a relatively rapid, transient, nerve impulse, having an
amplitude of roughly 100 mV and a duration of about 1 ms. In a
particular embodiment of a neural system having a series of
connected neurons (e.g., the transfer of spikes from one level of
neurons to another in FIG. 1), every action potential has basically
the same amplitude and duration, and thus, the information in the
signal may be represented only by the frequency and number of
spikes, or the time of spikes, rather than by the amplitude. The
information carried by an action potential may be determined by the
spike, the neuron that spiked, and the time of the spike relative
to other spike or spikes. The importance of the spike may be
determined by a weight applied to a connection between neurons, as
explained below.
[0034] The transfer of spikes from one level of neurons to another
may be achieved through the network of synaptic connections (or
simply "synapses") 104, as illustrated in FIG. 1. Relative to the
synapses 104, neurons of level 102 may be considered presynaptic
neurons and neurons of level 106 may be considered postsynaptic
neurons. The synapses 104 may receive output signals (i.e., spikes)
from the level 102 neurons and scale those signals according to
adjustable synaptic weights w.sub.1.sup.(i,i+1), . . . ,
w.sub.P.sup.(i,i+1) where P is a total number of synaptic
connections between the neurons of levels 102 and 106 and i is an
indicator of the neuron level. In the example of FIG. 1, i
represents neuron level 102 and i+1 represents neuron level 106.
Further, the scaled signals may be combined as an input signal of
each neuron in the level 106. Every neuron in the level 106 may
generate output spikes 110 based on the corresponding combined
input signal. The output spikes 110 may be transferred to another
level of neurons using another network of synaptic connections (not
shown in FIG. 1).
[0035] Biological synapses can mediate either excitatory or
inhibitory (hyperpolarizing) actions in postsynaptic neurons and
can also serve to amplify neuronal signals. Excitatory signals
depolarize the membrane potential (i.e., increase the membrane
potential with respect to the resting potential). If enough
excitatory signals are received within a certain time period to
depolarize the membrane potential above a threshold, an action
potential occurs in the postsynaptic neuron. In contrast,
inhibitory signals generally hyperpolarize (i.e., lower) the
membrane potential. Inhibitory signals, if strong enough, can
counteract the sum of excitatory signals and prevent the membrane
potential from reaching a threshold. In addition to counteracting
synaptic excitation, synaptic inhibition can exert powerful control
over spontaneously active neurons. A spontaneously active neuron
refers to a neuron that spikes without further input, for example
due to its dynamics or a feedback. By suppressing the spontaneous
generation of action potentials in these neurons, synaptic
inhibition can shape the pattern of firing in a neuron, which is
generally referred to as sculpturing. The various synapses 104 may
act as any combination of excitatory or inhibitory synapses,
depending on the behavior desired.
[0036] The neural system 100 may be emulated by a general purpose
processor, a digital signal processor (DSP), an application
specific integrated circuit (ASIC), a field programmable gate array
(FPGA) or other programmable logic device (PLD), discrete gate or
transistor logic, discrete hardware components, a software module
executed by a processor, or any combination thereof. The neural
system 100 may be utilized in a large range of applications, such
as image and pattern recognition, machine learning, motor control,
and alike. Each neuron in the neural system 100 may be implemented
as a neuron circuit. The neuron membrane charged to the threshold
value initiating the output spike may be implemented, for example,
as a capacitor that integrates an electrical current flowing
through it.
[0037] In an aspect, the capacitor may be eliminated as the
electrical current integrating device of the neuron circuit, and a
smaller memristor element may be used in its place. This approach
may be applied in neuron circuits, as well as in various other
applications where bulky capacitors are utilized as electrical
current integrators. In addition, each of the synapses 104 may be
implemented based on a memristor element, where synaptic weight
changes may relate to changes of the memristor resistance. With
nanometer feature-sized memristors, the area of a neuron circuit
and synapses may be substantially reduced, which may make
implementation of a large-scale neural system hardware
implementation more practical.
[0038] Functionality of a neural processor that emulates the neural
system 100 may depend on weights of synaptic connections, which may
control strengths of connections between neurons. The synaptic
weights may be stored in a non-volatile memory in order to preserve
functionality of the processor after being powered down. In an
aspect, the synaptic weight memory may be implemented on a separate
external chip from the main neural processor chip. The synaptic
weight memory may be packaged separately from the neural processor
chip as a replaceable memory card. This may provide diverse
functionalities to the neural processor, where a particular
functionality may be based on synaptic weights stored in a memory
card currently attached to the neural processor.
[0039] FIG. 2 illustrates an exemplary diagram 200 of a processing
unit (e.g., a neuron or neuron circuit) 202 of a computational
network (e.g., a neural system or a neural network) in accordance
with certain aspects of the present disclosure. For example, the
neuron 202 may correspond to any of the neurons of levels 102 and
106 from FIG. 1. The neuron 202 may receive multiple input signals
204.sub.1-204.sub.N, which may be signals external to the neural
system, or signals generated by other neurons of the same neural
system, or both. The input signal may be a current, a conductance,
a voltage, a real-valued, and/or a complex-valued. The input signal
may comprise a numerical value with a fixed-point or a
floating-point representation. These input signals may be delivered
to the neuron 202 through synaptic connections that scale the
signals according to adjustable synaptic weights
206.sub.1-206.sub.N (W.sub.1-W.sub.N), where N may be a total
number of input connections of the neuron 202.
[0040] The neuron 202 may combine the scaled input signals and use
the combined scaled inputs to generate an output signal 208 (i.e.,
a signal Y). The output signal 208 may be a current, a conductance,
a voltage, a real-valued and/or a complex-valued. The output signal
may be a numerical value with a fixed-point or a floating-point
representation. The output signal 208 may be then transferred as an
input signal to other neurons of the same neural system, or as an
input signal to the same neuron 202, or as an output of the neural
system.
[0041] The processing unit (neuron) 202 may be emulated by an
electrical circuit, and its input and output connections may be
emulated by electrical connections with synaptic circuits. The
processing unit 202 and its input and output connections may also
be emulated by a software code. The processing unit 202 may also be
emulated by an electric circuit, whereas its input and output
connections may be emulated by a software code. In an aspect, the
processing unit 202 in the computational network may be an analog
electrical circuit. In another aspect, the processing unit 202 may
be a digital electrical circuit. In yet another aspect, the
processing unit 202 may be a mixed-signal electrical circuit with
both analog and digital components. The computational network may
include processing units in any of the aforementioned forms. The
computational network (neural system or neural network) using such
processing units may be utilized in a large range of applications,
such as image and pattern recognition, machine learning, motor
control, and the like.
[0042] During the course of training a neural network, synaptic
weights (e.g., the weights w.sub.1.sup.(i,i+1), . . . ,
w.sub.P.sup.(i,i+1) from FIG. 1 and/or the weights
206.sub.1-206.sub.N from FIG. 2) may be initialized with random
values and increased or decreased according to a learning rule.
Those skilled in the art will appreciate that examples of the
learning rule include, but are not limited to the
spike-timing-dependent plasticity (STDP) learning rule, the Hebb
rule, the Oja rule, the Bienenstock-Copper-Munro (BCM) rule, etc.
In certain aspects, the weights may settle or converge to one of
two values (i.e., a bimodal distribution of weights). This effect
can be utilized to reduce the number of bits for each synaptic
weight, increase the speed of reading and writing from/to a memory
storing the synaptic weights, and to reduce power and/or processor
consumption of the synaptic memory.
Synapse Type
[0043] In hardware and software models of neural networks, the
processing of synapse related functions can be based on synaptic
type. Synapse types may be non-plastic synapses (no changes of
weight and delay), plastic synapses (weight may change), structural
delay plastic synapses (weight and delay may change), fully plastic
synapses (weight, delay and connectivity may change), and
variations thereupon (e.g., delay may change, but no change in
weight or connectivity). The advantage of multiple types is that
processing can be subdivided. For example, non-plastic synapses may
not require plasticity functions to be executed (or waiting for
such functions to complete). Similarly, delay and weight plasticity
may be subdivided into operations that may operate together or
separately, in sequence or in parallel. Different types of synapses
may have different lookup tables or formulas and parameters for
each of the different plasticity types that apply. Thus, the
methods would access the relevant tables, formulas, or parameters
for the synapse's type.
[0044] There are further implications of the fact that spike-timing
dependent structural plasticity may be executed independently of
synaptic plasticity. Structural plasticity may be executed even if
there is no change to weight magnitude (e.g., if the weight has
reached a minimum or maximum value, or it is not changed due to
some other reason) s structural plasticity (i.e., an amount of
delay change) may be a direct function of pre-post spike time
difference. Alternatively, structural plasticity may be set as a
function of the weight change amount or based on conditions
relating to bounds of the weights or weight changes. For example, a
synapse delay may change only when a weight change occurs or if
weights reach zero but not if they are at a maximum value. However,
it may be advantageous to have independent functions so that these
processes can be parallelized reducing the number and overlap of
memory accesses.
Determination of Synaptic Plasticity
[0045] Neuroplasticity (or simply "plasticity") is the capacity of
neurons and neural networks in the brain to change their synaptic
connections and behavior in response to new information, sensory
stimulation, development, damage, or dysfunction. Plasticity is
important to learning and memory in biology, as well as for
computational neuroscience and neural networks. Various forms of
plasticity have been studied, such as synaptic plasticity (e.g.,
according to the Hebbian theory), spike-timing-dependent plasticity
(STDP), non-synaptic plasticity, activity-dependent plasticity,
structural plasticity and homeostatic plasticity.
[0046] STDP is a learning process that adjusts the strength of
synaptic connections between neurons. The connection strengths are
adjusted based on the relative timing of a particular neuron's
output and received input spikes (i.e., action potentials). Under
the STDP process, long-term potentiation (LTP) may occur if an
input spike to a certain neuron tends, on average, to occur
immediately before that neuron's output spike. Then, that
particular input is made somewhat stronger. On the other hand,
long-term depression (LTD) may occur if an input spike tends, on
average, to occur immediately after an output spike. Then, that
particular input is made somewhat weaker, and hence the name
"spike-timing-dependent plasticity." Consequently, inputs that
might be the cause of the postsynaptic neuron's excitation are made
even more likely to contribute in the future, whereas inputs that
are not the cause of the postsynaptic spike are made less likely to
contribute in the future. The process continues until a subset of
the initial set of connections remains, while the influence of all
others is reduced to an insignificant level.
[0047] Because a neuron generally produces an output spike when
many of its inputs occur within a brief period (i.e., being
cumulative sufficient to cause the output), the subset of inputs
that typically remains includes those that tended to be correlated
in time. In addition, because the inputs that occur before the
output spike are strengthened, the inputs that provide the earliest
sufficiently cumulative indication of correlation will eventually
become the final input to the neuron.
[0048] The STDP learning rule may effectively adapt a synaptic
weight of a synapse connecting a presynaptic neuron to a
postsynaptic neuron as a function of time difference between spike
time t.sub.pre of the presynaptic neuron and spike time t.sub.post
of the postsynaptic neuron (i.e., t=t.sub.post-t.sub.pre). A
typical formulation of the STDP is to increase the synaptic weight
(i.e., potentiate the synapse) if the time difference is positive
(the presynaptic neuron fires before the postsynaptic neuron), and
decrease the synaptic weight (i.e., depress the synapse) if the
time difference is negative (the postsynaptic neuron fires before
the presynaptic neuron).
[0049] In the STDP process, a change of the synaptic weight over
time may be typically achieved using an exponential decay, as given
by:
.DELTA. w ( t ) = { a + - t / k + + .mu. , t > 0 a - t / k - , t
< 0 , ( 1 ) ##EQU00001##
where k.sub.+ and k.sub.- .tau..sub.sign(.DELTA.t) are time
constants for positive and negative time difference, respectively,
a.sub.+ and a.sub.- are corresponding scaling magnitudes, and .mu.
is an offset that may be applied to the positive time difference
and/or the negative time difference.
[0050] FIG. 3 illustrates an exemplary diagram 300 of a synaptic
weight change as a function of relative timing of presynaptic and
postsynaptic spikes in accordance with the STDP. If a presynaptic
neuron fires before a postsynaptic neuron, then a corresponding
synaptic weight may be increased, as illustrated in a portion 302
of the graph 300. This weight increase can be referred to as an LTP
of the synapse. It can be observed from the graph portion 302 that
the amount of LTP may decrease roughly exponentially as a function
of the difference between presynaptic and postsynaptic spike times.
The reverse order of firing may reduce the synaptic weight, as
illustrated in a portion 304 of the graph 300, causing an LTD of
the synapse.
[0051] As illustrated in the graph 300 in FIG. 3, a negative offset
.mu. may be applied to the LTP (causal) portion 302 of the STDP
graph. A point of cross-over 306 of the x-axis (y=0) may be
configured to coincide with the maximum time lag for considering
correlation for causal inputs from layer i-1. In the case of a
frame-based input (i.e., an input that is in the form of a frame of
a particular duration comprising spikes or pulses), the offset
value .mu. can be computed to reflect the frame boundary. A first
input spike (pulse) in the frame may be considered to decay over
time either as modeled by a postsynaptic potential directly or in
terms of the effect on neural state. If a second input spike
(pulse) in the frame is considered correlated or relevant to a
particular time frame, then the relevant times before and after the
frame may be separated at that time frame boundary and treated
differently in plasticity terms by offsetting one or more parts of
the STDP curve such that the value in the relevant times may be
different (e.g., negative for greater than one frame and positive
for less than one frame). For example, the negative offset .mu. may
be set to offset LTP such that the curve actually goes below zero
at a pre-post time greater than the frame time and it is thus part
of LTD instead of LTP.
Neuron Models and Operation
[0052] There are some general principles for designing a useful
spiking neuron model. A good neuron model may have rich potential
behavior in terms of two computational regimes: coincidence
detection and functional computation. Moreover, a good neuron model
should have two elements to allow temporal coding: arrival time of
inputs affects output time and coincidence detection can have a
narrow time window. Finally, to be computationally attractive, a
good neuron model may have a closed-form solution in continuous
time and stable behavior including near attractors and saddle
points. In other words, a useful neuron model is one that is
practical and that can be used to model rich, realistic and
biologically-consistent behaviors, as well as be used to both
engineer and reverse engineer neural circuits.
[0053] A neuron model may depend on events, such as an input
arrival, output spike or other event whether internal or external.
To achieve a rich behavioral repertoire, a state machine that can
exhibit complex behaviors may be desired. If the occurrence of an
event itself, separate from the input contribution (if any), can
influence the state machine and constrain dynamics subsequent to
the event, then the future state of the system is not only a
function of a state and input, but rather a function of a state,
event, and input.
[0054] In an aspect, a neuron n may be modeled as a spiking
leaky-integrate-and-fire neuron with a membrane voltage v.sub.n(t)
governed by the following dynamics:
v n ( t ) t = .alpha. v n ( t ) + .beta. m w m , n y m ( t -
.DELTA. t m , n ) , ( 2 ) ##EQU00002##
where .alpha. and .beta. are parameters, w.sub.m,n is a synaptic
weight for the synapse connecting a presynaptic neuron m to a
postsynaptic neuron n, and y.sub.m(t) is the spiking output of the
neuron m that may be delayed by dendritic or axonal delay according
to .DELTA.t.sub.m,n until arrival at the neuron n's soma.
[0055] It should be noted that there is a delay from the time when
sufficient input to a postsynaptic neuron is established until the
time when the postsynaptic neuron actually fires. In a dynamic
spiking neuron model, such as Izhikevich's simple model, a time
delay may be incurred if there is a difference between a
depolarization threshold v.sub.t and a peak spike voltage
v.sub.peak. For example, in the simple model, neuron soma dynamics
can be governed by the pair of differential equations for voltage
and recovery, i.e.:
v t = ( k ( v - v t ) ( v - v r ) - u + I ) / C , ( 3 ) u t = a ( b
( v - v r ) - u ) , ( 4 ) ##EQU00003##
where v is a membrane potential, u is a membrane recovery variable,
k is a parameter that describes time scale of the membrane
potential v, a is a parameter that describes time scale of the
recovery variable u, b is a parameter that describes sensitivity of
the recovery variable u to the sub-threshold fluctuations of the
membrane potential v, v.sub.r is a membrane resting potential, I is
a synaptic current, and C is a membrane's capacitance. In
accordance with this model, the neuron is defined to spike when
v>v.sub.peak.
Hunzinger Cold Model
[0056] The Hunzinger Cold neuron model is a minimal dual-regime
spiking linear dynamical model that can reproduce a rich variety of
neural behaviors. The model's one- or two-dimensional linear
dynamics can have two regimes, wherein the time constant (and
coupling) can depend on the regime. In the sub-threshold regime,
the time constant, negative by convention, represents leaky channel
dynamics generally acting to return a cell to rest in a
biologically-consistent linear fashion. The time constant in the
supra-threshold regime, positive by convention, reflects anti-leaky
channel dynamics generally driving a cell to spike while incurring
latency in spike-generation.
[0057] As illustrated in FIG. 4, the dynamics of the model 400 may
be divided into two (or more) regimes. These regimes may be called
the negative regime 402 (also interchangeably referred to as the
leaky-integrate-and-fire (LIF) regime, not to be confused with the
LIF neuron model) and the positive regime 404 (also interchangeably
referred to as the anti-leaky-integrate-and-fire (ALIF) regime, not
to be confused with the ALIF neuron model). In the negative regime
402, the state tends toward rest (v.sub.-) at the time of a future
event. In this negative regime, the model generally exhibits
temporal input detection properties and other sub-threshold
behavior. In the positive regime 404, the state tends toward a
spiking event (v.sub.s). In this positive regime, the model
exhibits computational properties, such as incurring a latency to
spike depending on subsequent input events. Formulation of dynamics
in terms of events and separation of the dynamics into these two
regimes are fundamental characteristics of the model.
[0058] Linear dual-regime bi-dimensional dynamics (for states v and
u) may be defined by convention as:
.tau. .rho. v t = v + q .rho. ( 5 ) - .tau. u u t = u + r , ( 6 )
##EQU00004##
where q.sub..rho. and r are the linear transformation variables for
coupling.
[0059] The symbol .rho. is used herein to denote the dynamics
regime with the convention to replace the symbol .rho. with the
sign "-" or "+" for the negative and positive regimes,
respectively, when discussing or expressing a relation for a
specific regime.
[0060] The model state is defined by a membrane potential (voltage)
v and recovery current u. In basic form, the regime is essentially
determined by the model state. There are subtle, but important
aspects of the precise and general definition, but for the moment,
consider the model to be in the positive regime 404 if the voltage
v is above a threshold (v.sub.+) and otherwise in the negative
regime 402.
[0061] The regime-dependent time constants include .tau..sub.-
which is the negative regime time constant, and .tau..sub.+ which
is the positive regime time constant. The recovery current time
constant .tau..sub.u is typically independent of regime. For
convenience, the negative regime time constant .tau..sub.- is
typically specified as a negative quantity to reflect decay so that
the same expression for voltage evolution may be used as for the
positive regime in which the exponent and .tau..sub.+ will
generally be positive, as will be .tau..sub.u.
[0062] The dynamics of the two state elements may be coupled at
events by transformations offsetting the states from their
null-clines, where the transformation variables are:
q.sub..rho.=-.tau..sub..rho..beta.u-v.sub..rho. (7)
r=.delta.(v+.epsilon.), (8)
where .delta., .epsilon., .beta. and v, v.sub.| are parameters. The
two values for v.sub..rho. are the base for reference voltages for
the two regimes. The parameter v.sub.- is the base voltage for the
negative regime, and the membrane potential will generally decay
toward v.sub.- in the negative regime. The parameter v.sub.+ is the
base voltage for the positive regime, and the membrane potential
will generally tend away from v.sub.+ in the positive regime.
[0063] The null-clines for v and u are given by the negative of the
transformation variables q.sub..rho. and r, respectively. The
parameter .delta. is a scale factor controlling the slope of the u
null-cline. The parameter .epsilon. is typically set equal to
-v.sub.-. The parameter .beta. is a resistance value controlling
the slope of the v null-clines in both regimes. The .tau..sub..rho.
time-constant parameters control not only the exponential decays,
but also the null-cline slopes in each regime separately.
[0064] The model may be defined to spike when the voltage v reaches
a value v.sub.S. Subsequently, the state may be reset at a reset
event (which may be one and the same as the spike event):
v={circumflex over (v)}.sub.- (9)
u=u+.DELTA.u, (10)
where {circumflex over (v)}.sub.- and .DELTA.u are parameters. The
reset voltage {circumflex over (v)}.sub.- is typically set to
v.sub.-.
[0065] By a principle of momentary coupling, a closed form solution
is possible not only for state (and with a single exponential
term), but also for the time to reach a particular state. The close
form state solutions are:
v ( t + .DELTA. t ) = ( v ( t ) + q .rho. ) .DELTA. t .tau. .rho. -
q .rho. ( 11 ) u ( t + .DELTA. t ) = ( u ( t ) + r ) - .DELTA. t
.tau. u - r . ( 12 ) ##EQU00005##
[0066] Therefore, the model state may be updated only upon events,
such as an input (presynaptic spike) or output (postsynaptic
spike). Operations may also be performed at any particular time
(whether or not there is input or output).
[0067] Moreover, by the momentary coupling principle, the time of a
postsynaptic spike may be anticipated so the time to reach a
particular state may be determined in advance without iterative
techniques or Numerical Methods (e.g., the Euler numerical method).
Given a prior voltage state v.sub.0, the time delay until voltage
state v.sub.f is reached is given by:
.DELTA. t = .tau. .rho. log v f + q .rho. v 0 + q .rho. . ( 13 )
##EQU00006##
[0068] If a spike is defined as occurring at the time the voltage
state v reaches v.sub.S, then the closed-form solution for the
amount of time, or relative delay, until a spike occurs as measured
from the time that the voltage is at a given state v is:
.DELTA. t S = { .tau. + log v S + q + v + q + if v > v ^ +
.infin. otherwise ( 14 ) ##EQU00007##
where {circumflex over (v)}.sub.+ is typically set to parameter
v.sub.+, although other variations may be possible.
[0069] The above definitions of the model dynamics depend on
whether the model is in the positive or negative regime. As
mentioned, the coupling and the regime .rho. may be computed upon
events. For purposes of state propagation, the regime and coupling
(transformation) variables may be defined based on the state at the
time of the last (prior) event. For purposes of subsequently
anticipating spike output time, the regime and coupling variable
may be defined based on the state at the time of the next (current)
event.
[0070] There are several possible implementations of the Cold
model, and executing the simulation, emulation or model in time.
This includes, for example, event-update, step-event update, and
step-update modes. An event update is an update where states are
updated based on events or "event update" (at particular moments).
A step update is an update when the model is updated at intervals
(e.g., 1 ms). This does not necessarily require iterative methods
or Numerical methods. An event-based implementation is also
possible at a limited time resolution in a step-based simulator by
only updating the model if an event occurs at or between steps or
by "step-event" update.
Neuronal Diversity and Pattern Classification
[0071] Aspects of the present disclosure are directed to providing
neuronal diversity (e.g., in hardware and neural simulation tools).
In one aspect, a value of a neuron parameter may be perturbed
across a set or population of neurons based on the value of the
parameter.
[0072] In accordance with an exemplary aspect of the present
disclosure, neurons may be used to implement neuronal diversity. In
this exemplary aspect of the present disclosure, neurons based on
the piecewise linear neuron model are used for ease of explanation.
This model may provide an efficient implementation of any
two-dimensional neuron model. However, other neural models such as
the COLD neural model, the Izhikevich (IZ) neural model and the
like may also be used directly. Neuron models that utilize larger
number of states, such as the Hodgkin-Huxley model or similar
number of states such as the Morris-Lecar model or smaller number
of states, such as the Leaky Integrate and Fire (LIF) models may
also be used.
[0073] Neuronal diversity may be increased by adjusting neural
parameters. In one aspect, a percentage range (e.g., +/-20%) of
perturbation around a mean value of the parameter may be specified.
For example, the resting membrane potential v.sub.rest may be
perturbed within a +/-20% range of a mean value for the resting
membrane potential v.sub.rest.
[0074] In a second example, a parameter .tau..sub.- may be
perturbed for a set of COLD neurons. Parameter .tau..sub.- is the
time constant of the decay of the membrane potential to the resting
potential v.sub.rest. In this example, .tau..sub.- may be perturbed
such that each neuron potentially uses a slightly different
.tau..sub.- parameter value than another neuron in the set.
[0075] In some aspects, the membrane potential v and the recovery
variable u may be adjusted to increase neuronal diversity. In some
aspects, a table of coefficients used in the update equations for v
and u (e.g., HVV, HVU, HVI, HVC, HUV, HUU, HUI, and HUC) may be
constructed. This may be beneficial as the coefficients alone may
be stored, thus enabling efficient processing because different
values of parameters may be computed without being stored.
[0076] The coefficients may be stored for different ranges of the
recovery variable v. For example, for a COLD neuron, two different
values for the coefficient HVV may be used. With respect to the LIF
model, one value may be used for the leaky integrate and fire (LIF)
regime and another value may be used for anti-leaky integrate and
fire (ALIF) regime. In some aspects, the value for these
coefficients may be computed based on the neuron model
parameters.
[0077] To increase neuronal diversity, perturbation may be applied
to the coefficients for the update equations. For instance, in some
aspects, the coefficients for membrane potential v and/or the
recovery variable u may be subjected to random perturbations. In
one example, the random perturbation may be applied to a neural
class for which diversity is desired as follows:
random_div_bits[8]={9,8,7,0,9,7,7,0} (15)
[0078] In this example, the random diversity bits
(random_div_bits[0-7] bits) may respectively correspond to
perturbation applied to coefficients HVV, HVU, HVI, HVC, HUV, HUU,
HUI, and HUC. Of course, the values of the random div bits [0-7]
are merely exemplary and not limiting.
[0079] In a further example, the perturbation may be applied to the
HVV coefficient as follows:
HVV_div=HVV+salt*HVV/2 (16-random_div_bits) (16)
where salt may be a random number between -1 and 1. In some
aspects, the salt value may be computed or generated at every tau
(.tau.) for each neuron using a neuron identifier (id) as a key for
a hash function. In other aspects, the salt value may be computed
or generated at events where a neuron state is updated. Thus, the
salt value for a given neuron may remain constant for the duration
of a simulation. This may be advantageous as the costly expense of
storing different H parameters may be reduced.
[0080] The random diversity bits (random_div_bits) may be used to
control the level of diversity on the H value (e.g., HVV or HUI).
For example, using a value of 9 may cause the H value to be
perturbed by a fraction of its value, where the fraction is chosen
randomly from the range [- 1/128, 1/128].
[0081] The level of diversity or perturbation may be controlled in
any number of ways. For example, in some aspects, the level of
perturbation may be controlled based on network behavior, input
statistics (e.g., temporal jitter, spurious spikes, background
noise level, drop in spikes), desired output, a desired probability
distribution, a level of diversity in spike time, a level of
diversity in synaptic weights, or other network and/or behavior
metrics.
[0082] As such, aspects of the present disclosure may beneficially
enable a user to control the level of diversity on each H value
(i.e., coefficient) individually. For example, perturbing one H
value (e.g., HVV) may be sufficient to provide a desired level of
neuronal diversity, such that diversity on other H values (e.g.,
HVI, HUU and HUI) is not implemented. As such, in accordance with
aspects of the present disclosure, neuronal parameters (e.g., HVV,
HVU, HVI, HVC, HUV, HUU, HUI, and HUC) may be perturbed
individually or in combination with varying degrees of
perturbation. Thus, the impact on each parameter may be
different.
[0083] In some aspects, the neural parameter perturbed may impact
the states of the neuron population. In one example, the HVV
parameter value may be based on .tau..sub.+ and .tau..sub.- values,
depending on ALIF or LIF regimes, respectively. Parameters
.tau..sub.+ and .tau..sub.- are the time constants of the membrane
potential. The firing rate across the population of the output
layer neurons with different levels of perturbation may be
uniformly distributed with HVV perturbation, and the range of the
distribution may increase with level of diversity. Moreover, in the
LIF regime, this parameter allows output layer neurons to spike
with different levels of input activity. Thus, some neurons with
smaller values of .tau..sub.- may spike only with higher coincident
input, while others with larger values of .tau..sub.- may spike
with only a small degree of coincident inputs.
[0084] As such, in some aspects, neuronal diversity may be
increased by adjusting the .tau..sub.- parameter. That is, because
.tau..sub.- controls the rate at which the membrane potential will
decay to resting potential, by varying .tau..sub.-, neurons may be
made less or more excitable to input.
[0085] In some aspects, parameter sweeps may be conducted to
determine the parameters, range of values and the like that may
further improve or even optimize neuronal diversity and performance
of the neural network. The parameter sweep may also be used to
determine whether one method of providing diversity (e.g., applying
random diversity bits) produces improved performance
characteristics over another method of providing diversity (e.g.,
dithering the least significant bit of a parameter). The parameters
deemed to provide improved performance may be stored and used to
train the neural network.
[0086] In another exemplary aspect, neuronal diversity may be
increased across a set or population of neurons by applying a
perturbation to a portion of a neuron parameter (e.g., H value(s)).
For example, neuronal diversity may be increased by
adding/subtracting a salt value that is unique to an individual
neuron to some specified least significant bits (LSBs) of the H
value. This approach allows a user to choose a level of
perturbation that is not proportional to the H value. Further,
additional calculation may achieve a zero-mean perturbation around
ideal values.
[0087] Increased neuronal diversity in accordance with aspects of
the present disclosure may be advantageous and broadly applicable.
In some aspects, by controlling neuronal diversity, the firing rate
across a population of neurons may likewise be controlled. For
example, the firing rate of a population of 100 neurons receiving
identical input from 1000 neurons may be varied using neuronal
diversity.
[0088] In one application of neuronal diversity, learning of
temporal patterns is made more robust to initial network
conditions. For example, the network may be configured to learn to
detect patterns in presence of noise in the form of spurious
spikes, dropped spikes, or temporal jitter in spike timing in the
pattern. The noise can be present in training as well as during a
testing phase. It should be appreciated that training a network in
the presence of spurious spikes, dropped spikes, or temporal jitter
in spike timing in the pattern enables correct classification of
real world patterns where parts of a signal may be missing (e.g.,
object may be occluded), noise signals may be present with the
signal of interest (e.g., background image along with an object of
interest), or temporal jitter may be present in the spike
representation of the object (e.g., blurry object).
[0089] In another exemplary aspect of the present disclosure,
diversity in spike latency may also be enhanced across a population
of neurons when these neurons receive identical inputs.
[0090] Furthermore, aspects of the present disclosure may
complement other mechanisms, such as the use of random weights and
random delays on synapses connecting the input layer to the output
layer. For example, when used in conjunction with spike
timing-dependent plasticity (STDP), the bi-modality in distribution
of weights may be reduced thereby making the learning more robust
to stochasticity in synaptic firing or loss of synapses. In
addition, performing parameter sweeps across different sets of
neuronal parameters may also be improved.
[0091] FIG. 5 illustrates an example implementation 500 of the
aforementioned providing neuronal diversity and pattern recognition
using a general-purpose processor 502 in accordance with certain
aspects of the present disclosure. Variables (neural signals),
synaptic weights, system parameters associated with a computational
network (neural network), delays, frequency bin information and
neural parameters may be stored in a memory block 504, while
instructions executed at the general-purpose processor 502 may be
loaded from a program memory 506. In an aspect of the present
disclosure, the instructions loaded into the general-purpose
processor 502 may comprise code for retrieving a set of parameters
for the set of neurons and/or perturbing the set of parameters
based on a neuron identification, level of perturbation and/or
parameter value.
[0092] In another aspect of the present disclosure, the
instructions loaded into the general-purpose processor 502 may
comprise code for creating a set of diverse neurons in a first
layer, presenting an input corresponding to a pattern plus noise at
an input layer, representing the input as spikes, receiving the
spikes at the first layer, spiking at the first layer based on the
received spikes, updating a weight of each synapses between input
layer neuron and output layer neuron based on spike timing
difference between a spike at the input layer neuron and a spike at
an output layer neuron, and classifying a spike pattern represented
by a set of inter-spike intervals, regardless of noise in the spike
pattern.
[0093] FIG. 6 illustrates an example implementation 600 of the
aforementioned providing neuronal diversity and pattern recognition
where a memory 602 can be interfaced via an interconnection network
604 with individual (distributed) processing units (neural
processors) 606 of a computational network (neural network) in
accordance with certain aspects of the present disclosure.
Variables (neural signals), synaptic weights, system parameters
associated with the computational network (neural network) delays,
frequency bin information, and neural parameters may be stored in
the memory 602, and may be loaded from the memory 602 via
connection(s) of the interconnection network 604 into each
processing unit (neural processor) 606. In an aspect of the present
disclosure, the processing unit 606 may be configured to retrieve a
set of parameters for the set of neurons and/or perturb the set of
parameters based on a neuron identification, level of perturbation
and/or parameter value.
[0094] In another aspect of the present disclosure, the processing
unit 606 may be configured to create a set of diverse neurons in a
first layer, present an input corresponding to a pattern plus noise
at an input layer, represent the input as spikes, receive the
spikes at the first layer, spike at the first layer based on the
received spikes, update a weight of each synapses between input
layer neuron and output layer neuron based on spike timing
difference between a spike at the input layer neuron and a spike at
an output layer neuron, and classify a spike pattern represented by
a set of inter-spike intervals, regardless of noise in the spike
pattern.
[0095] FIG. 7 illustrates an example implementation 700 of the
aforementioned providing neuronal diversity and pattern
recognition. As illustrated in FIG. 7, one memory bank 702 may be
directly interfaced with one processing unit 704 of a computational
network (neural network). Each memory bank 702 may store variables
(neural signals), synaptic weights, and/or system parameters
associated with a corresponding processing unit (neural processor)
704 delays, frequency bin information, and neuronal parameters. In
an aspect of the present disclosure, the processing unit 704 may be
configured to retrieve a set of parameters for the set of neurons
and/or perturb the set of parameters based on a neuron
identification, level of perturbation and/or parameter value.
[0096] In another aspect of the present disclosure, the processing
unit 704 may be configured to create a set of diverse neurons in a
first layer, present an input corresponding to a pattern plus noise
at an input layer, and represent the input as spikes, receive the
spikes at the first layer. The processing unit 704 is also
configured to spike at the first layer based on the received
spikes, update a weight of each synapses between input layer neuron
and output layer neuron based on spike timing difference between a
spike at the input layer neuron and a spike at an output layer
neuron, and classify a spike pattern represented by a set of
inter-spike intervals, regardless of noise in the spike
pattern.
[0097] FIG. 8 illustrates an example implementation of a neural
network 800 in accordance with certain aspects of the present
disclosure. As illustrated in FIG. 8, the neural network 800 may
have multiple local processing units 802 that may perform various
operations of methods described in the present disclosure. Each
local processing unit 802 may comprise a local state memory 804 and
a local parameter memory 806 that store parameters of the neural
network. In addition, the local processing unit 802 may have a
local (neuron) model program (LMP) memory 808 for storing a local
model program, a local learning program (LLP) memory 810 for
storing a local learning program, and a local connection memory
812. Furthermore, as illustrated in FIG. 8, each local processing
unit 802 may be interfaced with a configuration processor unit 814
for providing configurations for local memories of the local
processing unit, and with a routing unit 816 that provide routing
between the local processing units 802.
[0098] In one configuration, a neuron model is configured for
providing neuronal diversity. The neuron model includes a
retrieving means and perturbing means. In one aspect, the
retrieving means and/or perturbing means may be the general-purpose
processor 502, program memory 506, memory block 504, memory 602,
interconnection network 604, processing units 606, processing unit
704, local processing units 802, and or the routing connection
processing elements 816 configured to perform the functions
recited. In another configuration, the aforementioned means may be
any module or any apparatus configured to perform the functions
recited by the aforementioned means.
[0099] In another configuration, a neuron model is configured for
pattern recognition. The neuron model includes a creating means,
presenting means, receiving means, spiking means, updating means,
and/or classifying means. In one aspect, the creating means,
presenting means, receiving means, spiking means, updating means,
and/or classifying means may be the general-purpose processor 502,
program memory 506, memory block 504, memory 602, interconnection
network 604, processing units 606, processing unit 704, local
processing units 802, and or the routing connection processing
elements 816 configured to perform the functions recited. In
another configuration, the aforementioned means may be any module
or any apparatus configured to perform the functions recited by the
aforementioned means.
[0100] According to certain aspects of the present disclosure, each
local processing unit 802 may be configured to determine parameters
of the neural network based upon desired one or more functional
features of the neural network, and develop the one or more
functional features towards the desired functional features as the
determined parameters are further adapted, tuned and updated.
[0101] FIG. 9A is a block diagram illustrating an exemplary neural
network 900 implementing neural diversity in accordance with
aspects of the present disclosure. Referring to FIG. 9A, the
exemplary neural network is configured as a spiking neural network.
The neural network 900 includes a classifier 902. The classifier
may be configured with an input layer 904 and an output layer 906.
Parameters of the neurons in the input layer and/or the output
layer may be perturbed to implement neuronal diversity. Although
the classifier of FIG. 9A includes two layers, this is merely
exemplary, for ease of illustration and explanation, and not
limiting.
[0102] The input layer 904 and output layer 906 may be coupled
together via synaptic connections 910. In some aspects, the
synaptic connections 910 may be configured such that the neurons of
the input layer 904 and neurons of the output layer 906 may be
connected in an all-to-all fashion. By virtue of the all-to-all
connectivity between inputs and output layer neurons, each of the
neurons of the output layer 906 may receive similar inputs (e.g.,
the same inputs). As such, spikes (e.g., 908a, 908b, 908c, and
908d) received at the input layer 904 may present the same input to
each of the neurons of the output layer 906. However, because of
the implemented neuronal diversity, the output layer neurons may
generate a spike (912a, 912b, 912c) at different times.
[0103] In some aspects, diversity may also be applied to the
weights of synaptic connections 910 in a manner similar to that
described above with respect to neurons. For example, a weight
(e.g., W.sub.i) of one or more of the synaptic connections 910 or
synapses connecting two neurons may be a function of the spike
timing difference (e.g., spike timing-dependent plasticity (STDP)).
Applying diversity, the spike timings may be made diverse and in
turn, the weight updates for the synaptic connections 910 may be
made diverse.
[0104] As shown in FIG. 9B, by applying diversity, output spike
timings to.sub.1 and t.sub.o2 may be made diverse. The weight
updates on the synapses connecting the k.sup.th input layer neuron
and j.sup.th output layer neuron may be based on difference in the
spike timings t.sub.oj-t.sub.ik. An exemplary schematic function is
shown in FIG. 9B. In the exemplary schematic, the weight update
(dW) is positive for a causal input spike and negative for a
non-causal input spike. Further, the higher the coincidence, (or
the smaller the difference in spike times), the larger the
magnitude of the weight update (dW). Thus, when output layer spike
timings are made diverse across different output layer neurons
using neuronal diversity, the weight updates on synapses connecting
an input layer neuron to different output layer neurons may also be
made diverse if the weight update function is not a constant.
[0105] FIG. 10 is a block diagram illustrating an exemplary neural
network 1000 using neural diversity in accordance with aspects of
the present disclosure. Referring to FIG. 10, the neural network is
configured for pattern classification. The neural network includes
a classifier 1010 having an input layer 1012 and a classification
layer 1014. Inputs may be supplied to the classifier via input
1002, which may convert an input to spikes, for example. A pattern
of spikes (e.g., 1004) in the presence of noise spikes 1006 may be
presented to the input layer 1012 of the classifier.
[0106] A set of neurons in the input layer 1012 and/or the
classification layer 1014 may be configured as diverse set by
applying diversity. In some aspects, the spike timing may also be
made diverse. As such, weight of the synaptic connection between a
neuron of the input layer 1012 and a neuron of the classification
layer 1014 may be updated such that the classifier 1010 may learn
to generate spikes when a pattern (e.g., represented by spikes
1004) is presented at the classification layer 1014.
[0107] In some aspects, the pattern classification may be based on
inter-spike intervals between the spikes representing the pattern.
In this case, spikes representing the pattern are presented during
an interval T ms (e.g., 100 ms). That is, the pattern is
represented by the inter-spike interval for spikes 1004 during the
T ms. As such, the neurons of the classification layer 1014 may be
trained to generate spikes according to the inter-spike interval
between pattern spikes 1004 during T ms of pattern input. Thus,
neurons of the classification layer 1014 may generate spikes 1008
at timings corresponding to the pattern presentation interval
(e.g., T ms), and in doing so, a pattern may be classified even in
the presence of noise.
[0108] In one example, the pattern classification may be achieved
by learning weights on the synapses connecting the input layer and
the output layer of the neural network 1010 such that the output
layer neurons generate a spike only when the pattern is presented
at the input layer and not otherwise. When output layer neurons
have diverse parameters and spike at different times for the same
input, for certain synaptic weight update functions, the weights
are updated such that neurons spike for different (possibly
non-contiguous) parts of the pattern. For example, when the
membrane potential decay time constant at the output layer neuron
is large, the first few spikes of the input spike pattern may be
sufficient to cause a spike at the output layer neuron. Similarly,
when the membrane potential decay time constant at the output layer
neuron is small, only a coincident part of the input spike pattern
may cause a spike at the output layer neuron. The diversity in
spike times and the resulting diversity in weight updates allows
distortions around the ideal pattern to be detected. For instance,
if parts of the pattern are missing, or if the inter spike interval
between the spikes representing the spikes are jittered (e.g., due
to blurry input), the diversity in weights allows the output layer
to still generate spiking outputs for the input pattern and enable
detection.
[0109] By implementing diversity, the classifier is able to detect
portions of a pattern rather than merely detecting the earliest
part of a pattern that results in a classification. For example, a
numerical classifier configured without diversity may not be able
to distinguish a number `3` from a number `8` given the similar
form. As a result, misclassification errors may be incurred.
However, by implementing neuronal diversity, all subparts of the
pattern may be used to determine the classification, thereby
reducing misclassification errors.
[0110] FIG. 11 illustrates a method 1100 for providing neuronal
diversity in a set of neurons. In block 1102, the neuron model
retrieves a set of parameters for the set of neurons. Furthermore,
in block 1104, the neuron model perturbs the set of parameters
based on a neuron identification value, level of perturbation for
each parameter and/or parameter value.
[0111] In some aspects, the set of parameters may be perturbed
based on a percentage range of perturbation around a mean value of
one or more parameter values in the set. In other aspects, the set
of parameters may be perturbed by dithering a least significant bit
of a parameter value for a portion of the set of neurons.
[0112] The level of perturbation for each parameter and or
parameter value may also be controlled. In some aspects, the level
of perturbation may be based on network behavior and input
statistics. For example, the level of perturbation may be selected
based on the presence of spurious spikes, temporal jitter,
background noise and or a drop in input spikes or the like.
Further, in some aspects, the level of perturbation may be based on
a desired output, a desired probability distribution and/or a level
of diversity in spike time or synaptic weight.
[0113] FIG. 12 illustrates a method 1200 for pattern recognition in
a spiking neural network. In block 1202, the neuron model creates a
set of diverse neurons in a first layer to increase diversity in a
set of spike timings. In some aspects, the first layer may comprise
a classification layer or an intermediate layer.
[0114] In block 1204, the neuron model presents an input
corresponding to a pattern plus noise at an input layer. The noise
may include, for example, spurious spikes, dropped spikes, and/or
temporal jitter in the spike pattern.
[0115] In block 1206, the neuron model represents the input as
spikes. In block 1208, the neuron model receives the spikes at the
first layer. In block 1210, the neuron model spikes at the first
layer based on the received spikes.
[0116] In block 1212, the neuron model updates a weight for each
synapse between an input layer neuron and output layer neuron based
on spike timing differences between a spike at the input layer
neuron and a spike at an output layer neuron. In some aspects, the
weight is spike timing modulated with updates. The spike timing may
be different in response to the same input. Further, in some
aspects, a diverse set of weight updates may be achieved based on
synapses between two layers for a same input.
[0117] In block 1214, the neuron model classifies a spike pattern
represented by a set of inter-spike intervals, regardless of noise
in the spike pattern.
[0118] In some aspects, the neuron model may further train synapses
between the input layer and a classification layer based on the
spike pattern and spike timing differences between two layers.
[0119] The various operations of methods described above may be
performed by any suitable means capable of performing the
corresponding functions. The means may include various hardware
and/or software component(s) and/or module(s), including, but not
limited to, a circuit, an application specific integrated circuit
(ASIC), or processor. Generally, where there are operations
illustrated in the figures, those operations may have corresponding
counterpart means-plus-function components with similar
numbering.
[0120] As used herein, the term "determining" encompasses a wide
variety of actions. For example, "determining" may include
calculating, computing, processing, deriving, investigating,
looking up (e.g., looking up in a table, a database or another data
structure), ascertaining and the like. Additionally, "determining"
may include receiving (e.g., receiving information), accessing
(e.g., accessing data in a memory) and the like. Furthermore,
"determining" may include resolving, selecting, choosing,
establishing and the like.
[0121] As used herein, a phrase referring to "at least one of" a
list of items refers to any combination of those items, including
single members. As an example, "at least one of: a, b, or c" is
intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c.
[0122] The various illustrative logical blocks, modules and
circuits described in connection with the present disclosure may be
implemented or performed with a general purpose processor, a
digital signal processor (DSP), an application specific integrated
circuit (ASIC), a field programmable gate array signal (FPGA) or
other programmable logic device (PLD), discrete gate or transistor
logic, discrete hardware components or any combination thereof
designed to perform the functions described herein. A
general-purpose processor may be a microprocessor, but in the
alternative, the processor may be any commercially available
processor, controller, microcontroller or state machine. A
processor may also be implemented as a combination of computing
devices, e.g., a combination of a DSP and a microprocessor, a
plurality of microprocessors, one or more microprocessors in
conjunction with a DSP core, or any other such configuration.
[0123] The steps of a method or algorithm described in connection
with the present disclosure may be embodied directly in hardware,
in a software module executed by a processor, or in a combination
of the two. A software module may reside in any form of storage
medium that is known in the art. Some examples of storage media
that may be used include random access memory (RAM), read only
memory (ROM), flash memory, erasable programmable read-only memory
(EPROM), electrically erasable programmable read-only memory
(EEPROM), registers, a hard disk, a removable disk, a CD-ROM and so
forth. A software module may comprise a single instruction, or many
instructions, and may be distributed over several different code
segments, among different programs, and across multiple storage
media. A storage medium may be coupled to a processor such that the
processor can read information from, and write information to, the
storage medium. In the alternative, the storage medium may be
integral to the processor.
[0124] The methods disclosed herein comprise one or more steps or
actions for achieving the described method. The method steps and/or
actions may be interchanged with one another without departing from
the scope of the claims. In other words, unless a specific order of
steps or actions is specified, the order and/or use of specific
steps and/or actions may be modified without departing from the
scope of the claims.
[0125] The functions described may be implemented in hardware,
software, firmware, or any combination thereof. If implemented in
hardware, an example hardware configuration may comprise a
processing system in a device. The processing system may be
implemented with a bus architecture. The bus may include any number
of interconnecting buses and bridges depending on the specific
application of the processing system and the overall design
constraints. The bus may link together various circuits including a
processor, machine-readable media, and a bus interface. The bus
interface may be used to connect a network adapter, among other
things, to the processing system via the bus. The network adapter
may be used to implement signal processing functions. For certain
aspects, a user interface (e.g., keypad, display, mouse, joystick,
etc.) may also be connected to the bus. The bus may also link
various other circuits such as timing sources, peripherals, voltage
regulators, power management circuits, and the like, which are well
known in the art, and therefore, will not be described any
further.
[0126] The processor may be responsible for managing the bus and
general processing, including the execution of software stored on
the machine-readable media. The processor may be implemented with
one or more general-purpose and/or special-purpose processors.
Examples include microprocessors, microcontrollers, DSP processors,
and other circuitry that can execute software. Software shall be
construed broadly to mean instructions, data, or any combination
thereof, whether referred to as software, firmware, middleware,
microcode, hardware description language, or otherwise.
Machine-readable media may include, by way of example, random
access memory (RAM), flash memory, read only memory (ROM),
programmable read-only memory (PROM), erasable programmable
read-only memory (EPROM), electrically erasable programmable
Read-only memory (EEPROM), registers, magnetic disks, optical
disks, hard drives, or any other suitable storage medium, or any
combination thereof. The machine-readable media may be embodied in
a computer-program product. The computer-program product may
comprise packaging materials.
[0127] In a hardware implementation, the machine-readable media may
be part of the processing system separate from the processor.
However, as those skilled in the art will readily appreciate, the
machine-readable media, or any portion thereof, may be external to
the processing system. By way of example, the machine-readable
media may include a transmission line, a carrier wave modulated by
data, and/or a computer product separate from the device, all which
may be accessed by the processor through the bus interface.
Alternatively, or in addition, the machine-readable media, or any
portion thereof, may be integrated into the processor, such as the
case may be with cache and/or general register files. Although the
various components discussed may be described as having a specific
location, such as a local component, they may also be configured in
various ways, such as certain components being configured as part
of a distributed computing system.
[0128] The processing system may be configured as a general-purpose
processing system with one or more microprocessors providing the
processor functionality and external memory providing at least a
portion of the machine-readable media, all linked together with
other supporting circuitry through an external bus architecture.
Alternatively, the processing system may comprise one or more
neuromorphic processors for implementing the neuron models and
models of neural systems described herein. As another alternative,
the processing system may be implemented with an application
specific integrated circuit (ASIC) with the processor, the bus
interface, the user interface, supporting circuitry, and at least a
portion of the machine-readable media integrated into a single
chip, or with one or more field programmable gate arrays (FPGAs),
programmable logic devices (PLDs), controllers, state machines,
gated logic, discrete hardware components, or any other suitable
circuitry, or any combination of circuits that can perform the
various functionality described throughout this disclosure. Those
skilled in the art will recognize how best to implement the
described functionality for the processing system depending on the
particular application and the overall design constraints imposed
on the overall system.
[0129] The machine-readable media may comprise a number of software
modules. The software modules include instructions that, when
executed by the processor, cause the processing system to perform
various functions. The software modules may include a transmission
module and a receiving module. Each software module may reside in a
single storage device or be distributed across multiple storage
devices. By way of example, a software module may be loaded into
RAM from a hard drive when a triggering event occurs. During
execution of the software module, the processor may load some of
the instructions into cache to increase access speed. One or more
cache lines may then be loaded into a general register file for
execution by the processor. When referring to the functionality of
a software module below, it will be understood that such
functionality is implemented by the processor when executing
instructions from that software module.
[0130] If implemented in software, the functions may be stored or
transmitted over as one or more instructions or code on a
computer-readable medium. Computer-readable media include both
computer storage media and communication media including any medium
that facilitates transfer of a computer program from one place to
another. A storage medium may be any available medium that can be
accessed by a computer. By way of example, and not limitation, such
computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or
other optical disk storage, magnetic disk storage or other magnetic
storage devices, or any other medium that can be used to carry or
store desired program code in the form of instructions or data
structures and that can be accessed by a computer. In addition, any
connection is properly termed a computer-readable medium. For
example, if the software is transmitted from a website, server, or
other remote source using a coaxial cable, fiber optic cable,
twisted pair, digital subscriber line (DSL), or wireless
technologies such as infrared (IR), radio, and microwave, then the
coaxial cable, fiber optic cable, twisted pair, DSL, or wireless
technologies such as infrared, radio, and microwave are included in
the definition of medium. Disk and disc, as used herein, include
compact disc (CD), laser disc, optical disc, digital versatile disc
(DVD), floppy disk, and Blu-ray.RTM. disc where disks usually
reproduce data magnetically, while discs reproduce data optically
with lasers. Thus, in some aspects computer-readable media may
comprise non-transitory computer-readable media (e.g., tangible
media). In addition, for other aspects computer-readable media may
comprise transitory computer-readable media (e.g., a signal).
Combinations of the above should also be included within the scope
of computer-readable media.
[0131] Thus, certain aspects may comprise a computer program
product for performing the operations presented herein. For
example, such a computer program product may comprise a
computer-readable medium having instructions stored (and/or
encoded) thereon, the instructions being executable by one or more
processors to perform the operations described herein. For certain
aspects, the computer program product may include packaging
material.
[0132] Further, it should be appreciated that modules and/or other
appropriate means for performing the methods and techniques
described herein can be downloaded and/or otherwise obtained by a
user terminal and/or base station as applicable. For example, such
a device can be coupled to a server to facilitate the transfer of
means for performing the methods described herein. Alternatively,
various methods described herein can be provided via storage means
(e.g., RAM, ROM, a physical storage medium such as a compact disc
(CD) or floppy disk, etc.), such that a user terminal and/or base
station can obtain the various methods upon coupling or providing
the storage means to the device. Moreover, any other suitable
technique for providing the methods and techniques described herein
to a device can be utilized.
[0133] It is to be understood that the claims are not limited to
the precise configuration and components illustrated above. Various
modifications, changes and variations may be made in the
arrangement, operation and details of the methods and apparatus
described above without departing from the scope of the claims.
* * * * *